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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.analysis.solvers;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.NoBracketingException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.TooManyEvaluationsException;<a name="line.21"></a>
<FONT color="green">022</FONT>    <a name="line.22"></a>
<FONT color="green">023</FONT>    /**<a name="line.23"></a>
<FONT color="green">024</FONT>     * Implements the &lt;a href="http://mathworld.wolfram.com/RiddersMethod.html"&gt;<a name="line.24"></a>
<FONT color="green">025</FONT>     * Ridders' Method&lt;/a&gt; for root finding of real univariate functions. For<a name="line.25"></a>
<FONT color="green">026</FONT>     * reference, see C. Ridders, &lt;i&gt;A new algorithm for computing a single root<a name="line.26"></a>
<FONT color="green">027</FONT>     * of a real continuous function &lt;/i&gt;, IEEE Transactions on Circuits and<a name="line.27"></a>
<FONT color="green">028</FONT>     * Systems, 26 (1979), 979 - 980.<a name="line.28"></a>
<FONT color="green">029</FONT>     * &lt;p&gt;<a name="line.29"></a>
<FONT color="green">030</FONT>     * The function should be continuous but not necessarily smooth.&lt;/p&gt;<a name="line.30"></a>
<FONT color="green">031</FONT>     *<a name="line.31"></a>
<FONT color="green">032</FONT>     * @version $Id: RiddersSolver.java 1379560 2012-08-31 19:40:30Z erans $<a name="line.32"></a>
<FONT color="green">033</FONT>     * @since 1.2<a name="line.33"></a>
<FONT color="green">034</FONT>     */<a name="line.34"></a>
<FONT color="green">035</FONT>    public class RiddersSolver extends AbstractUnivariateSolver {<a name="line.35"></a>
<FONT color="green">036</FONT>        /** Default absolute accuracy. */<a name="line.36"></a>
<FONT color="green">037</FONT>        private static final double DEFAULT_ABSOLUTE_ACCURACY = 1e-6;<a name="line.37"></a>
<FONT color="green">038</FONT>    <a name="line.38"></a>
<FONT color="green">039</FONT>        /**<a name="line.39"></a>
<FONT color="green">040</FONT>         * Construct a solver with default accuracy (1e-6).<a name="line.40"></a>
<FONT color="green">041</FONT>         */<a name="line.41"></a>
<FONT color="green">042</FONT>        public RiddersSolver() {<a name="line.42"></a>
<FONT color="green">043</FONT>            this(DEFAULT_ABSOLUTE_ACCURACY);<a name="line.43"></a>
<FONT color="green">044</FONT>        }<a name="line.44"></a>
<FONT color="green">045</FONT>        /**<a name="line.45"></a>
<FONT color="green">046</FONT>         * Construct a solver.<a name="line.46"></a>
<FONT color="green">047</FONT>         *<a name="line.47"></a>
<FONT color="green">048</FONT>         * @param absoluteAccuracy Absolute accuracy.<a name="line.48"></a>
<FONT color="green">049</FONT>         */<a name="line.49"></a>
<FONT color="green">050</FONT>        public RiddersSolver(double absoluteAccuracy) {<a name="line.50"></a>
<FONT color="green">051</FONT>            super(absoluteAccuracy);<a name="line.51"></a>
<FONT color="green">052</FONT>        }<a name="line.52"></a>
<FONT color="green">053</FONT>        /**<a name="line.53"></a>
<FONT color="green">054</FONT>         * Construct a solver.<a name="line.54"></a>
<FONT color="green">055</FONT>         *<a name="line.55"></a>
<FONT color="green">056</FONT>         * @param relativeAccuracy Relative accuracy.<a name="line.56"></a>
<FONT color="green">057</FONT>         * @param absoluteAccuracy Absolute accuracy.<a name="line.57"></a>
<FONT color="green">058</FONT>         */<a name="line.58"></a>
<FONT color="green">059</FONT>        public RiddersSolver(double relativeAccuracy,<a name="line.59"></a>
<FONT color="green">060</FONT>                             double absoluteAccuracy) {<a name="line.60"></a>
<FONT color="green">061</FONT>            super(relativeAccuracy, absoluteAccuracy);<a name="line.61"></a>
<FONT color="green">062</FONT>        }<a name="line.62"></a>
<FONT color="green">063</FONT>    <a name="line.63"></a>
<FONT color="green">064</FONT>        /**<a name="line.64"></a>
<FONT color="green">065</FONT>         * {@inheritDoc}<a name="line.65"></a>
<FONT color="green">066</FONT>         */<a name="line.66"></a>
<FONT color="green">067</FONT>        @Override<a name="line.67"></a>
<FONT color="green">068</FONT>        protected double doSolve()<a name="line.68"></a>
<FONT color="green">069</FONT>            throws TooManyEvaluationsException,<a name="line.69"></a>
<FONT color="green">070</FONT>                   NoBracketingException {<a name="line.70"></a>
<FONT color="green">071</FONT>            double min = getMin();<a name="line.71"></a>
<FONT color="green">072</FONT>            double max = getMax();<a name="line.72"></a>
<FONT color="green">073</FONT>            // [x1, x2] is the bracketing interval in each iteration<a name="line.73"></a>
<FONT color="green">074</FONT>            // x3 is the midpoint of [x1, x2]<a name="line.74"></a>
<FONT color="green">075</FONT>            // x is the new root approximation and an endpoint of the new interval<a name="line.75"></a>
<FONT color="green">076</FONT>            double x1 = min;<a name="line.76"></a>
<FONT color="green">077</FONT>            double y1 = computeObjectiveValue(x1);<a name="line.77"></a>
<FONT color="green">078</FONT>            double x2 = max;<a name="line.78"></a>
<FONT color="green">079</FONT>            double y2 = computeObjectiveValue(x2);<a name="line.79"></a>
<FONT color="green">080</FONT>    <a name="line.80"></a>
<FONT color="green">081</FONT>            // check for zeros before verifying bracketing<a name="line.81"></a>
<FONT color="green">082</FONT>            if (y1 == 0) {<a name="line.82"></a>
<FONT color="green">083</FONT>                return min;<a name="line.83"></a>
<FONT color="green">084</FONT>            }<a name="line.84"></a>
<FONT color="green">085</FONT>            if (y2 == 0) {<a name="line.85"></a>
<FONT color="green">086</FONT>                return max;<a name="line.86"></a>
<FONT color="green">087</FONT>            }<a name="line.87"></a>
<FONT color="green">088</FONT>            verifyBracketing(min, max);<a name="line.88"></a>
<FONT color="green">089</FONT>    <a name="line.89"></a>
<FONT color="green">090</FONT>            final double absoluteAccuracy = getAbsoluteAccuracy();<a name="line.90"></a>
<FONT color="green">091</FONT>            final double functionValueAccuracy = getFunctionValueAccuracy();<a name="line.91"></a>
<FONT color="green">092</FONT>            final double relativeAccuracy = getRelativeAccuracy();<a name="line.92"></a>
<FONT color="green">093</FONT>    <a name="line.93"></a>
<FONT color="green">094</FONT>            double oldx = Double.POSITIVE_INFINITY;<a name="line.94"></a>
<FONT color="green">095</FONT>            while (true) {<a name="line.95"></a>
<FONT color="green">096</FONT>                // calculate the new root approximation<a name="line.96"></a>
<FONT color="green">097</FONT>                final double x3 = 0.5 * (x1 + x2);<a name="line.97"></a>
<FONT color="green">098</FONT>                final double y3 = computeObjectiveValue(x3);<a name="line.98"></a>
<FONT color="green">099</FONT>                if (FastMath.abs(y3) &lt;= functionValueAccuracy) {<a name="line.99"></a>
<FONT color="green">100</FONT>                    return x3;<a name="line.100"></a>
<FONT color="green">101</FONT>                }<a name="line.101"></a>
<FONT color="green">102</FONT>                final double delta = 1 - (y1 * y2) / (y3 * y3);  // delta &gt; 1 due to bracketing<a name="line.102"></a>
<FONT color="green">103</FONT>                final double correction = (FastMath.signum(y2) * FastMath.signum(y3)) *<a name="line.103"></a>
<FONT color="green">104</FONT>                                          (x3 - x1) / FastMath.sqrt(delta);<a name="line.104"></a>
<FONT color="green">105</FONT>                final double x = x3 - correction;                // correction != 0<a name="line.105"></a>
<FONT color="green">106</FONT>                final double y = computeObjectiveValue(x);<a name="line.106"></a>
<FONT color="green">107</FONT>    <a name="line.107"></a>
<FONT color="green">108</FONT>                // check for convergence<a name="line.108"></a>
<FONT color="green">109</FONT>                final double tolerance = FastMath.max(relativeAccuracy * FastMath.abs(x), absoluteAccuracy);<a name="line.109"></a>
<FONT color="green">110</FONT>                if (FastMath.abs(x - oldx) &lt;= tolerance) {<a name="line.110"></a>
<FONT color="green">111</FONT>                    return x;<a name="line.111"></a>
<FONT color="green">112</FONT>                }<a name="line.112"></a>
<FONT color="green">113</FONT>                if (FastMath.abs(y) &lt;= functionValueAccuracy) {<a name="line.113"></a>
<FONT color="green">114</FONT>                    return x;<a name="line.114"></a>
<FONT color="green">115</FONT>                }<a name="line.115"></a>
<FONT color="green">116</FONT>    <a name="line.116"></a>
<FONT color="green">117</FONT>                // prepare the new interval for next iteration<a name="line.117"></a>
<FONT color="green">118</FONT>                // Ridders' method guarantees x1 &lt; x &lt; x2<a name="line.118"></a>
<FONT color="green">119</FONT>                if (correction &gt; 0.0) {             // x1 &lt; x &lt; x3<a name="line.119"></a>
<FONT color="green">120</FONT>                    if (FastMath.signum(y1) + FastMath.signum(y) == 0.0) {<a name="line.120"></a>
<FONT color="green">121</FONT>                        x2 = x;<a name="line.121"></a>
<FONT color="green">122</FONT>                        y2 = y;<a name="line.122"></a>
<FONT color="green">123</FONT>                    } else {<a name="line.123"></a>
<FONT color="green">124</FONT>                        x1 = x;<a name="line.124"></a>
<FONT color="green">125</FONT>                        x2 = x3;<a name="line.125"></a>
<FONT color="green">126</FONT>                        y1 = y;<a name="line.126"></a>
<FONT color="green">127</FONT>                        y2 = y3;<a name="line.127"></a>
<FONT color="green">128</FONT>                    }<a name="line.128"></a>
<FONT color="green">129</FONT>                } else {                            // x3 &lt; x &lt; x2<a name="line.129"></a>
<FONT color="green">130</FONT>                    if (FastMath.signum(y2) + FastMath.signum(y) == 0.0) {<a name="line.130"></a>
<FONT color="green">131</FONT>                        x1 = x;<a name="line.131"></a>
<FONT color="green">132</FONT>                        y1 = y;<a name="line.132"></a>
<FONT color="green">133</FONT>                    } else {<a name="line.133"></a>
<FONT color="green">134</FONT>                        x1 = x3;<a name="line.134"></a>
<FONT color="green">135</FONT>                        x2 = x;<a name="line.135"></a>
<FONT color="green">136</FONT>                        y1 = y3;<a name="line.136"></a>
<FONT color="green">137</FONT>                        y2 = y;<a name="line.137"></a>
<FONT color="green">138</FONT>                    }<a name="line.138"></a>
<FONT color="green">139</FONT>                }<a name="line.139"></a>
<FONT color="green">140</FONT>                oldx = x;<a name="line.140"></a>
<FONT color="green">141</FONT>            }<a name="line.141"></a>
<FONT color="green">142</FONT>        }<a name="line.142"></a>
<FONT color="green">143</FONT>    }<a name="line.143"></a>




























































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